4a^2-5a-125=0

Solution for 4a^2-5a-125=0 equation:

Simplifying
4a2 + -5a + -125 = 0

Reorder the terms:
-125 + -5a + 4a2 = 0

Solving
-125 + -5a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -1a)(25 + -4a) = 0

Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
Set the factor '(25 + -4a)' equal to zero and attempt to solve:

Simplifying
25 + -4a = 0

Solving
25 + -4a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-25' to each side of the equation.
25 + -25 + -4a = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -4a = 0 + -25
-4a = 0 + -25

Combine like terms: 0 + -25 = -25
-4a = -25

Divide each side by '-4'.
a = 6.25

Simplifying
a = 6.25
Solution
a = {-5, 6.25}